A force acts in the direction ⟨4, 2⟩, moving an object along a straight path from (2, –4) to (10, 1). How much work is done by the force?

The displacement is ⟨10 − 2, 1 − (−4)⟩ = ⟨8, 5⟩. Work is the dot product of the force and displacement: ⟨4, 2⟩ · ⟨8, 5⟩ = 4(8) + 2(5) = 42 joules. So the answer is 42 joules.

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